Complexity develops via the incorporation of innovative properties. Chess is
one of the most complex strategy games, where expert contenders exercise
decision making by imitating old games or introducing innovations. In this
work, we study innovation in chess by analyzing how different move sequences
are played at the population level. It is found that the probability of
exploring a new or innovative move decreases as a power law with the frequency
of the preceding move sequence. Chess players also exploit already known move
sequences according to their frequencies, following a preferential growth
mechanism. Furthermore, innovation in chess exhibits Heaps' law suggesting
similarities with the process of vocabulary growth. We propose a robust
generative mechanism based on nested Yule-Simon preferential growth processes
that reproduces the empirical observations. These results, supporting the
self-similar nature of innovations in chess are important in the context of
decision making in a competitive scenario, and extend the scope of relevant
findings recently discovered regarding the emergence of Zipf's law in chess.Comment: 8 pages, 4 figures, accepted for publication in Europhysics Letters
(EPL